6a^2+21a=10a+35

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Solution for 6a^2+21a=10a+35 equation: 


Simplifying
6a2 + 21a = 10a + 35

Reorder the terms:
21a + 6a2 = 10a + 35

Reorder the terms:
21a + 6a2 = 35 + 10a

Solving
21a + 6a2 = 35 + 10a

Solving for variable 'a'.

Reorder the terms:
-35 + 21a + -10a + 6a2 = 35 + 10a + -35 + -10a

Combine like terms: 21a + -10a = 11a
-35 + 11a + 6a2 = 35 + 10a + -35 + -10a

Reorder the terms:
-35 + 11a + 6a2 = 35 + -35 + 10a + -10a

Combine like terms: 35 + -35 = 0
-35 + 11a + 6a2 = 0 + 10a + -10a
-35 + 11a + 6a2 = 10a + -10a

Combine like terms: 10a + -10a = 0
-35 + 11a + 6a2 = 0

Factor a trinomial.
(-7 + -2a)(5 + -3a) = 0


Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve:

Simplifying
-7 + -2a = 0

Solving
-7 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -2a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2a = 0 + 7
-2a = 0 + 7

Combine like terms: 0 + 7 = 7
-2a = 7

Divide each side by '-2'.
a = -3.5

Simplifying
a = -3.5

Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-3.5, 1.666666667}

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